[Dune] Help requested for my first test case in non linear mechanics

[HELFER Thomas 202608]

Dear Dune users,

I introduced my self by saying that I was interested to evaluate Dune for non linear mechanics
and in particular that I wanted to use MFront behaviours in Dune.

I tried to adapt the poisson-solver example given by O. Sander to the description of a simple
tensile test on a unit cube.

It almost works. I can simulate a tensile test for an elastic behaviour and a plastic behaviour.
I probably can use any smal strain behaviour generated by MFront. The non-linearity is treated
very crudely as we use an Newton algorithm with a fixed number of iterations.

The trouble is that it only works if the grid contains only a single element. This probably means
that I made a mistake in the assembly of the stiffness matrix or the assembly of the inner
forces. I reread my code several times without finding the trouble.

Please find enclosed my project, modified to drop the dependency to the MGIS library and
only integrate an isotropic elastic behaviour. The relevant file is
dune-mgis/src/dune-mgis-tensile-test.cc.

The purpose of my request is twofold:

- I would be grateful if anyone could find what I have done wrong.
- I would be grateful if anyone could review the code to tell me what could be improved.

With kind regards,

Thomas Helfer
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